Simple features

Simple features (sf) is an open standard developed and endorsed by the Open Geospatial Consortium (OGC). Sf is a hierarchical data model that represents a wide range of geometry types. Of 18 geometry types supported by the specification, only 7 are used in the vast majority of geographic research (see figure below); these core geometry types are fully supported by the R package sf (Pebesma 2018).

Simple feature types fully supported by sf

sf can represent all common vector geometry types (raster data classes are not supported by sf): points, lines, polygons and their respective ‘multi’ versions (which group together features of the same type into a single feature). sf also supports geometry collections, which can contain multiple geometry types in a single object. sf provides the same functionality (and more) previously provided in three packages — sp for data classes [@R-sp], rgdal for data read/write via an interface to GDAL and PROJ [@R-rgdal] and rgeos for spatial operations via an interface to GEOS [@R-rgeos].

sf’s functionality is well documented on its website at r-spatial.github.io/sf/ which contains 7 vignettes. These can be viewed offline as follows:

vignette(package = "sf") # see which vignettes are available
vignette("sf1")          # an introduction to the package

As the first vignette explains, simple feature objects in R are stored in a data frame, with geographic data occupying a special column, usually named ‘geom’ or ‘geometry’. We will use the world dataset provided by spData, loaded at the beginning of this chapter, to show what sf objects and how they work. world is an ‘sf data frame’ containing spatial and attribute columns, the names of which are returned by the function names() (the last column in this example contains the geographic information):

class(world)

## [1] "sf"         "tbl_df"     "tbl"        "data.frame"

names(world)

##  [1] "iso_a2"    "name_long" "continent" "region_un" "subregion" "type"     
##  [7] "area_km2"  "pop"       "lifeExp"   "gdpPercap" "geom"

The contents of this geom column give sf objects their spatial powers: world$geom is a ‘list column’ that contains all the coordinates of the country polygons. sf objects can be plotted quickly with the base R function plot(); the following command creates the figure below:

plot(world)

A spatial plot of the world using the sf package, with a facet for each attribute.

Note that instead of creating a single map by default for geographic objects, as most GIS programs do, plot()ing sf objects results in a map for each variable in the datasets. This behavior can be useful for exploring the spatial distribution of different variables and is discussed furthe in a later section.

More broadly, treating geographic objects as regular data frames with spatial powers has many advantages, especially if you are already used to working with data frames. The commonly used summary() function, for example, provides a useful overview of the variables within the world object.

summary(world["lifeExp"])

##     lifeExp                 geom    
##  Min.   :50.62   MULTIPOLYGON :177  
##  1st Qu.:64.96   epsg:4326    :  0  
##  Median :72.87   +proj=long...:  0  
##  Mean   :70.85                      
##  3rd Qu.:76.78                      
##  Max.   :83.59                      
##  NA's   :10

Although we have only selected one variable for the summary() command, it also outputs a report on the geometry. This demonstrates the ‘sticky’ behavior of the geometry columns of sf objects, meaning the geometry is kept unless the user deliberately removes them. The result provides a quick summary of both the non-spatial and spatial data contained in world: the mean average life expectancy is 71 years (ranging from less than 51 to more than 83 years with a median of 73 years) across all countries.

It is worth taking a deeper look at the basic behavior and contents of this simple feature object, which can usefully be thought of as a ‘spatial data frame’.

sf objects are easy to subset: the code below shows how to return an object containing only the first two rows and the first three columns of the world object. The output shows two major differences compared with a regular data.frame: the inclusion of additional geographic metadata (Geometry type, Dimension, Bounding box and coordinate reference system information on the line beginning Geodetic CRS CRS information), and the presence of a ‘geometry column’, here named geom:

world_mini = world[1:2, 1:3]
world_mini

## Simple feature collection with 2 features and 3 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: -180 ymin: -18.28799 xmax: 180 ymax: -0.95
## Geodetic CRS:  WGS 84
## # A tibble: 2 × 4
##   iso_a2 name_long continent                                                geom
##   <chr>  <chr>     <chr>                                      <MULTIPOLYGON [°]>
## 1 FJ     Fiji      Oceania   (((-180 -16.55522, -179.9174 -16.50178, -179.7933 …
## 2 TZ     Tanzania  Africa    (((33.90371 -0.95, 31.86617 -1.02736, 30.76986 -1.…

All this may seem rather complex, especially for a class system that is supposed to be ‘simple’! However, there are good reasons for organizing things this way and using sf to work with vector geographic datasets.

Before describing each geometry type that the sf package supports, it is worth taking a step back to understand the building blocks of sf objects.

• Simple features objects are data frames, with special geometry columns.
  • These spatial columns are often called geom or geometry: world$geom refers to the spatial element of the world object described above.
  • These geometry columns are ‘list columns’ of class sfc
  • In turn, sfc objects are composed of one or more objects of class sfg: simple feature geometries

To understand how the spatial components of simple features work, it is vital to understand simple feature geometries.

Why simple features?

Simple features is a widely supported data model that underlies data structures in many GIS applications including QGIS and PostGIS. A major advantage of this is that using the data model ensures your work is cross-transferable to other set-ups, for example importing from and exporting to spatial databases.

A more specific question from an R perspective is “why use the sf package when sp is already tried and tested”? There are many reasons (linked to the advantages of the simple features model):

• Fast reading and writing of data
• Enhanced plotting performance
• sf objects can be treated as data frames in most operations
• sf function names are relatively consistent and intuitive (all begin with st_)
• sf functions can be combined with the |> operator and works well with the tidyverse collection of R packages.

sf’s support for tidyverse packages is exemplified by read_sf(), a function for importing geographic vector data Unlike the function st_read(), which returns attributes stored in a base R data.frame (and which emits verbose messages, not shown in the code chunk below), read_sf() silently returns data as a tidyverse tibble. This is demonstrated below:

world_dfr = st_read(system.file("shapes/world.shp", package = "spData"))

## Reading layer `world' from data source 
##   `/Library/Frameworks/R.framework/Versions/4.1/Resources/library/spData/shapes/world.shp' 
##   using driver `ESRI Shapefile'
## Simple feature collection with 177 features and 10 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: -180 ymin: -89.9 xmax: 180 ymax: 83.64513
## Geodetic CRS:  WGS 84

world_tbl = read_sf(system.file("shapes/world.shp", package = "spData"))
class(world_dfr)

## [1] "sf"         "data.frame"

class(world_tbl)

## [1] "sf"         "tbl_df"     "tbl"        "data.frame"

sf is now the go-to package for analysis of spatial vector data in R. spatstat, a package ecosystem which provides numerous functions for spatial statistics, and terra both have vector geographic data classes, but neither have the same level of uptake as sf does for working with vector data. Many popular packages build on sf. Transitioning established packages and workflows away from legacy packages rgeos and rgdal takes time (Bivand 2021), but the process was given a sense of urgency by messages printed when they were loaded, which state that they “will be retired by the end of 2023”. This means that anyone still using these packages should “transition to sf/stars/terra functions using GDAL and PROJ at your earliest convenience”.

In other words, sf is future proof but sp is not. For workflows that depend on the legacy class system, sf objects can be converted from and to the Spatial class of the sp package as follows:

library(sp)
world_sp = as(world, "Spatial") # from an sf object to sp
# sp functions ...
world_sf = st_as_sf(world_sp)           # from sp to sf

Basic map making

Basic maps are created in sf with plot(). By default this creates a multi-panel plot, one sub-plot for each variable of the object, as illustrated in the left-hand panel in the figure below. A legend or ‘key’ with a continuous color is produced if the object to be plotted has a single variable (see the right-hand panel). Colors can also be set with col =, although this will not create a continuous palette or a legend.

plot(world[3:6])
plot(world["pop"])

Plotting with sf, with multiple variables (left) and a single variable (right).

Plots are added as layers to existing images by setting add = TRUE.¹ To demonstrate this, and to provide a insight on attribute and spatial data operations, the subsequent code chunk filters countries in Asia and combines them into a single feature:

world_asia = world[world$continent == "Asia", ]
asia = st_union(world_asia)

We can now plot the Asian continent over a map of the world. Note that the first plot must only have one facet for add = TRUE to work. If the first plot has a key, reset = FALSE must be used:

plot(world["pop"], reset = FALSE)
plot(asia, add = TRUE, col = "red")

A plot of Asia added as a layer on top of countries worldwide.

Adding layers in this way can be used to verify the geographic correspondence between layers: the plot() function is fast to execute and requires few lines of code, but does not create interactive maps with a wide range of options. For more advanced map making we recommend using dedicated visualization packages such as tmap

There are various ways to modify maps with sf’s plot() method. Because sf extends base R plotting methods plot()’s arguments such as main = (which specifies the title of the map) work with sf objects (see ?graphics::plot and ?par).²

The figure below illustrates this flexibility by overlaying circles, whose diameters (set with cex =) represent country populations, on a map of the world.

plot(world["continent"], reset = FALSE)
cex = sqrt(world$pop) / 10000
world_cents = st_centroid(world, of_largest = TRUE)
plot(st_geometry(world_cents), add = TRUE, cex = cex)

Country continents (represented by fill color) and 2015 populations (represented by circles, with area proportional to population).

The code above uses the function st_centroid() to convert one geometry type (polygons) to another (points) , the aesthetics of which are varied with the cex argument.

sf’s plot method also has arguments specific to geographic data. expandBB, for example, can be used to plot an sf object in context: it takes a numeric vector of length four that expands the bounding box of the plot relative to zero in the following order: bottom, left, top, right. This is used to plot India in the context of its giant Asian neighbors, with an emphasis on China to the east, in the following code chunk, visualized in the following figure

india = world[world$name_long == "India", ]
plot(st_geometry(india), expandBB = c(0, 0.2, 0.1, 1), col = "gray", lwd = 3)
plot(st_geometry(world_asia), add = TRUE)

India in context, demonstrating the expandBB argument.

Note the use of lwd to emphasize India in the plotting code.

Geometry types

Geometries are the basic building blocks of simple features. Simple features in R can take on one of the 18 geometry types supported by the sf package. In this section we will focus on the seven most commonly used types: POINT, LINESTRING, POLYGON, MULTIPOINT, MULTILINESTRING, MULTIPOLYGON and GEOMETRYCOLLECTION. Find the whole list of possible feature types in the PostGIS manual.

Generally, well-known binary (WKB) or well-known text (WKT) are the standard encoding for simple feature geometries. WKB representations are usually hexadecimal strings easily readable for computers. This is why GIS and spatial databases use WKB to transfer and store geometry objects. WKT, on the other hand, is a human-readable text markup description of simple features. Both formats are exchangeable, and if we present one, we will naturally choose the WKT representation.

The basis for each geometry type is the point. A point is simply a coordinate in 2D, 3D or 4D space (see vignette("sf1") for more information) such as (see left panel in Figure below:

• POINT (5 2)

A linestring is a sequence of points with a straight line connecting the points, for example (see middle panel in Figure below:

• LINESTRING (1 5, 4 4, 4 1, 2 2, 3 2)

A polygon is a sequence of points that form a closed, non-intersecting ring. Closed means that the first and the last point of a polygon have the same coordinates (see right panel in Figure below.) By definition, a polygon has one exterior boundary (outer ring) and can have zero or more interior boundaries (inner rings), also known as holes. A polygon with a hole would be, for example, POLYGON ((1 5, 2 2, 4 1, 4 4, 1 5), (2 4, 3 4, 3 3, 2 3, 2 4))

• Polygon without a hole: POLYGON ((1 5, 2 2, 4 1, 4 4, 1 5))

Illustration of point, linestring and polygon geometries.

So far we have created geometries with only one geometric entity per feature. sf also allows multiple geometries of a single type to exist within a single feature within “multi” version of each geometry type:

• Multipoint: MULTIPOINT (5 2, 1 3, 3 4, 3 2)
• Multilinestring: MULTILINESTRING ((1 5, 4 4, 4 1, 2 2, 3 2), (1 2, 2 4))
• Multipolygon: MULTIPOLYGON (((1 5, 2 2, 4 1, 4 4, 1 5), (0 2, 1 2, 1 3, 0 3, 0 2)))

Illustration of multi* geometries.

Finally, a geometry collection can contain any combination of geometries including (multi)points and linestrings (see Figure below):

• Geometry collection: GEOMETRYCOLLECTION (MULTIPOINT (5 2, 1 3, 3 4, 3 2), LINESTRING (1 5, 4 4, 4 1, 2 2, 3 2))

Illustration of a geometry collection.

The sf class

Simple features consist of two main parts: geometries and non-geographic attributes. Figure below shows how an sf object is created – geometries come from an sfc object, while attributes are taken from a data.frame or tibble.

Building blocks of sf objects.

Non-geographic attributes represent the name of the feature or other attributes such as measured values, groups, and other things. To illustrate attributes, we will represent a temperature of 25°C in London on June 21^st, 2017. This example contains a geometry (the coordinates), and three attributes with three different classes (place name, temperature and date). Objects of class sf represent such data by combining the attributes (data.frame) with the simple feature geometry column (sfc). They are created with st_sf() as illustrated below, which creates the London example described above:

lnd_point = st_point(c(0.1, 51.5))                 # sfg object
lnd_geom = st_sfc(lnd_point, crs = 4326)           # sfc object
lnd_attrib = data.frame(                           # data.frame object
  name = "London",
  temperature = 25,
  date = as.Date("2017-06-21")
  )
lnd_sf = st_sf(lnd_attrib, geometry = lnd_geom)    # sf object

What just happened? First, the coordinates were used to create the simple feature geometry (sfg). Second, the geometry was converted into a simple feature geometry column (sfc), with a CRS. Third, attributes were stored in a data.frame, which was combined with the sfc object with st_sf(). This results in an sf object, as demonstrated below (some output is omitted):

lnd_sf
#> Simple feature collection with 1 features and 3 fields
#> ...
#>     name temperature       date         geometry
#> 1 London          25 2017-06-21 POINT (0.1 51.5)

class(lnd_sf)

## [1] "sf"         "data.frame"

The result shows that sf objects actually have two classes, sf and data.frame. Simple features are simply data frames (square tables), but with spatial attributes stored in a list column, usually called geometry, as previousl described. This duality is central to the concept of simple features: most of the time a sf can be treated as and behaves like a data.frame. Simple features are, in essence, data frames with a spatial extension.

Simple feature geometries (sfg)

The sfg class represents the different simple feature geometry types in R: point, linestring, polygon (and their ‘multi’ equivalents, such as multipoints) or geometry collection.

Usually you are spared the tedious task of creating geometries on your own since you can simply import an already existing spatial file. However, there are a set of functions to create simple feature geometry objects (sfg) from scratch if needed. The names of these functions are simple and consistent, as they all start with the st_ prefix and end with the name of the geometry type in lowercase letters:

• A point: st_point()
• A linestring: st_linestring()
• A polygon: st_polygon()
• A multipoint: st_multipoint()
• A multilinestring: st_multilinestring()
• A multipolygon: st_multipolygon()
• A geometry collection: st_geometrycollection()

sfg objects can be created from three base R data types:

1. A numeric vector: a single point
2. A matrix: a set of points, where each row represents a point, a multipoint or linestring
3. A list: a collection of objects such as matrices, multilinestrings or geometry collections

The function st_point() creates single points from numeric vectors:

st_point(c(5, 2))                 # XY point

## POINT (5 2)

st_point(c(5, 2, 3))              # XYZ point

## POINT Z (5 2 3)

st_point(c(5, 2, 1), dim = "XYM") # XYM point

## POINT M (5 2 1)

st_point(c(5, 2, 3, 1))           # XYZM point

## POINT ZM (5 2 3 1)

The results show that XY (2D coordinates), XYZ (3D coordinates) and XYZM (3D with an additional variable, typically measurement accuracy) point types are created from vectors of length 2, 3, and 4, respectively. The XYM type must be specified using the dim argument (which is short for dimension).

By contrast, use matrices in the case of multipoint (st_multipoint()) and linestring (st_linestring()) objects:

# the rbind function simplifies the creation of matrices
## MULTIPOINT
multipoint_matrix = rbind(c(5, 2), c(1, 3), c(3, 4), c(3, 2))
st_multipoint(multipoint_matrix)

## MULTIPOINT ((5 2), (1 3), (3 4), (3 2))

## LINESTRING
linestring_matrix = rbind(c(1, 5), c(4, 4), c(4, 1), c(2, 2), c(3, 2))
st_linestring(linestring_matrix)

## LINESTRING (1 5, 4 4, 4 1, 2 2, 3 2)

Finally, use lists for the creation of multilinestrings, (multi-)polygons and geometry collections:

## POLYGON
polygon_list = list(rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5)))
st_polygon(polygon_list)

## POLYGON ((1 5, 2 2, 4 1, 4 4, 1 5))

## POLYGON with a hole
polygon_border = rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5))
polygon_hole = rbind(c(2, 4), c(3, 4), c(3, 3), c(2, 3), c(2, 4))
polygon_with_hole_list = list(polygon_border, polygon_hole)
st_polygon(polygon_with_hole_list)

## POLYGON ((1 5, 2 2, 4 1, 4 4, 1 5), (2 4, 3 4, 3 3, 2 3, 2 4))

## MULTILINESTRING
multilinestring_list = list(rbind(c(1, 5), c(4, 4), c(4, 1), c(2, 2), c(3, 2)), 
                            rbind(c(1, 2), c(2, 4)))
st_multilinestring((multilinestring_list))

## MULTILINESTRING ((1 5, 4 4, 4 1, 2 2, 3 2), (1 2, 2 4))

## MULTIPOLYGON
multipolygon_list = list(list(rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5))),
                         list(rbind(c(0, 2), c(1, 2), c(1, 3), c(0, 3), c(0, 2))))
st_multipolygon(multipolygon_list)

## MULTIPOLYGON (((1 5, 2 2, 4 1, 4 4, 1 5)), ((0 2, 1 2, 1 3, 0 3, 0 2)))

## GEOMETRYCOLLECTION
geometrycollection_list = list(st_multipoint(multipoint_matrix),
                              st_linestring(linestring_matrix))
st_geometrycollection(geometrycollection_list)
#> GEOMETRYCOLLECTION (MULTIPOINT (5 2, 1 3, 3 4, 3 2),
#>   LINESTRING (1 5, 4 4, 4 1, 2 2, 3 2))

Simple feature columns (sfc)

One sfg object contains only a single simple feature geometry. A simple feature geometry column (sfc) is a list of sfg objects, which is additionally able to contain information about the coordinate reference system in use. For instance, to combine two simple features into one object with two features, we can use the st_sfc() function.

This is important since sfc represents the geometry column in sf data frames:

# sfc POINT
point1 = st_point(c(5, 2))
point2 = st_point(c(1, 3))
points_sfc = st_sfc(point1, point2)
points_sfc

## Geometry set for 2 features 
## Geometry type: POINT
## Dimension:     XY
## Bounding box:  xmin: 1 ymin: 2 xmax: 5 ymax: 3
## CRS:           NA

## POINT (5 2)

## POINT (1 3)

In most cases, an sfc object contains objects of the same geometry type. Therefore, when we convert sfg objects of type polygon into a simple feature geometry column, we would also end up with an sfc object of type polygon, which can be verified with st_geometry_type(). Equally, a geometry column of multilinestrings would result in an sfc object of type multilinestring:

# sfc POLYGON
polygon_list1 = list(rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5)))
polygon1 = st_polygon(polygon_list1)
polygon_list2 = list(rbind(c(0, 2), c(1, 2), c(1, 3), c(0, 3), c(0, 2)))
polygon2 = st_polygon(polygon_list2)
polygon_sfc = st_sfc(polygon1, polygon2)
st_geometry_type(polygon_sfc)

## [1] POLYGON POLYGON
## 18 Levels: GEOMETRY POINT LINESTRING POLYGON MULTIPOINT ... TRIANGLE

# sfc MULTILINESTRING
multilinestring_list1 = list(rbind(c(1, 5), c(4, 4), c(4, 1), c(2, 2), c(3, 2)), 
                            rbind(c(1, 2), c(2, 4)))
multilinestring1 = st_multilinestring((multilinestring_list1))
multilinestring_list2 = list(rbind(c(2, 9), c(7, 9), c(5, 6), c(4, 7), c(2, 7)), 
                            rbind(c(1, 7), c(3, 8)))
multilinestring2 = st_multilinestring((multilinestring_list2))
multilinestring_sfc = st_sfc(multilinestring1, multilinestring2)
st_geometry_type(multilinestring_sfc)

## [1] MULTILINESTRING MULTILINESTRING
## 18 Levels: GEOMETRY POINT LINESTRING POLYGON MULTIPOINT ... TRIANGLE

It is also possible to create an sfc object from sfg objects with different geometry types:

# sfc GEOMETRY
point_multilinestring_sfc = st_sfc(point1, multilinestring1)
st_geometry_type(point_multilinestring_sfc)

## [1] POINT           MULTILINESTRING
## 18 Levels: GEOMETRY POINT LINESTRING POLYGON MULTIPOINT ... TRIANGLE

As mentioned before, sfc objects can additionally store information on the coordinate reference systems (CRS). The default value is NA (Not Available), as can be verified with st_crs():

st_crs(points_sfc)

## Coordinate Reference System: NA

All geometries in sfc objects must have the same CRS. A CRS can be specified with the crs argument of st_sfc() (or st_sf()), which takes a CRS identifier provided as a text string, such as crs = "EPSG:4326"

# Set the CRS with an identifier referring to an 'EPSG' CRS code:
points_sfc_wgs = st_sfc(point1, point2, crs = "EPSG:4326")
st_crs(points_sfc_wgs) # print CRS (only first 4 lines of output shown)
#> Coordinate Reference System:
#>   User input: EPSG:4326 
#>   wkt:
#> GEOGCRS["WGS 84",
#> ...

R packages for working with raster data

Over the last two decades, several packages for reading and processing raster datasets have been developed. As outlined in Section, chief among them was raster, which led to a step change in R’s raster capabilities when it was launched in 2010 and the premier package in the space until the development of terra and stars. Both more recently developed package provide powerful and performant functions for working with raster datasets and there is substantial overlap between their possible use cases. In this book we focus on terra, which replaces the older and (in most cases) slower raster. Before learning about the how terra’s class system works, this section describes similarities and differences between terra and stars; this knowledge will help decide which is most appropriate in different situations.

First, terra focuses on the most common raster data model (regular grids), while stars also allows storing less popular models (including regular, rotated, sheared, rectilinear, and curvilinear grids). While terra usually handles one or multi-layered rasters³, the stars package provides ways to store raster data cubes – a raster object with many layers (e.g., bands), for many moments in time (e.g., months), and many attributes (e.g., sensor type A and sensor type B). Importantly, in both packages, all layers or elements of a data cube must have the same spatial dimensions and extent. Second, both packages allow to either read all of the raster data into memory or just to read its metadata – this is usually done automatically based on the input file size. However, they store raster values very differently. terra is based on C++ code and mostly uses C++ pointers. stars stores values as lists of arrays for smaller rasters or just a file path for larger ones. Third, stars functions are closely related to the vector objects and functions in sf, while terra uses its own class of objects for vector data, namely SpatVector. Fourth, both packages have a different approach for how various functions work on their objects. The terra package mostly relies on a large number of built-in functions, where each function has a specific purpose (e.g., resampling or cropping). On the other hand, stars uses some build-in functions (usually with names starting with st_), has its own methods for existing R functions (e.g., split() or aggregate()), and also for existing dplyr functions (e.g., filter() or slice()).

Importantly, it is straightforward to convert objects from terra to stars (using st_as_stars()) and the other way round (using rast()). We also encourage you to read @pebesma_spatial_2022 for the most comprehensive introduction to the stars package.

An introduction to terra

The terra package supports raster objects in R. Like its predecessor raster (created by the same developer, Robert Hijmans), it provides an extensive set of functions to create, read, export, manipulate and process raster datasets. terra’s functionality is largely the same as the more mature raster package, but there are some differences: terra functions are usually more computationally efficient than raster equivalents. On the other hand, the raster class system is popular and used by many other packages. You can seamlessly translate between the two types of object to ensure backwards compatibility with older scripts and packages, for example, with the functions raster(), stack(), and brick() in the raster package (see the previous chapter for more on the evolution of R packages for working with geographic data).

In addition to functions for raster data manipulation, terra provides many low-level functions that can form a foundation for developing new tools for working with raster datasets.

terra also lets you work on large raster datasets that are too large to fit into the main memory. In this case, terra provides the possibility to divide the raster into smaller chunks, and processes these iteratively instead of loading the whole raster file into RAM.

For the illustration of terra concepts, we will use datasets from the spDataLarge. It consists of a few raster objects and one vector object covering an area of the Zion National Park (Utah, USA). For example, srtm.tif is a digital elevation model of this area (for more details, see its documentation ?srtm). First, let’s create a SpatRaster object named my_rast:

raster_filepath = system.file("raster/srtm.tif", package = "spDataLarge")
my_rast = rast(raster_filepath)
class(my_rast)

## [1] "SpatRaster"
## attr(,"package")
## [1] "terra"

Typing the name of the raster into the console, will print out the raster header (dimensions, resolution, extent, CRS) and some additional information (class, data source, summary of the raster values):

my_rast

## class       : SpatRaster 
## dimensions  : 457, 465, 1  (nrow, ncol, nlyr)
## resolution  : 0.0008333333, 0.0008333333  (x, y)
## extent      : -113.2396, -112.8521, 37.13208, 37.51292  (xmin, xmax, ymin, ymax)
## coord. ref. : lon/lat WGS 84 (EPSG:4326) 
## source      : srtm.tif 
## name        : srtm 
## min value   : 1024 
## max value   : 2892

Dedicated functions report each component: dim() returns the number of rows, columns and layers; ncell() the number of cells (pixels); res() the spatial resolution; ext() its spatial extent; and crs() its coordinate reference system. inMemory() reports whether the raster data is stored in memory or on disk.

help("terra-package") returns a full list of all available terra functions.

Basic map making

Similar to the sf package, terra also provides plot() methods for its own classes.

plot(my_rast)

Basic raster plot.

There are several other approaches for plotting raster data in R that are outside the scope of this section, including:

• plotRGB() function from the terra package to create a Red-Green-Blue plot based on three layers in a SpatRaster object
• Packages such as tmap to create static and interactive maps of raster and vector objects
• Functions, for example levelplot() from the rasterVis package, to create facets, a common technique for visualizing change over time

Raster classes

The SpatRaster class represents rasters object in terra. The easiest way to create a raster object in R is to read-in a raster file from disk or from a server .

single_raster_file = system.file("raster/srtm.tif", package = "spDataLarge")
single_rast = rast(raster_filepath)

The terra package supports numerous drivers with the help of the GDAL library. Rasters from files are usually not read entirely into RAM, with an exception of their header and a pointer to the file itself.

Rasters can also be created from scratch using the same rast() function. This is illustrated in the subsequent code chunk, which results in a new SpatRaster object. The resulting raster consists of 36 cells (6 columns and 6 rows specified by nrows and ncols) centered around the Prime Meridian and the Equator (see xmin, xmax, ymin and ymax parameters). The default CRS of raster objects is WGS84, but can be changed with the crs argument. This means the unit of the resolution is in degrees which we set to 0.5 (resolution). Values (vals) are assigned to each cell: 1 to cell 1, 2 to cell 2, and so on. Remember: rast() fills cells row-wise (unlike matrix()) starting at the upper left corner, meaning the top row contains the values 1 to 6, the second 7 to 12, etc.

new_raster = rast(nrows = 6, ncols = 6, resolution = 0.5, 
                  xmin = -1.5, xmax = 1.5, ymin = -1.5, ymax = 1.5,
                  vals = 1:36)

For other ways of creating raster objects, see ?rast.

The SpatRaster class also handles multiple layers, which typically correspond to a single multispectral satellite file or a time-series of rasters.

multi_raster_file = system.file("raster/landsat.tif", package = "spDataLarge")
multi_rast = rast(multi_raster_file)
multi_rast

## class       : SpatRaster 
## dimensions  : 1428, 1128, 4  (nrow, ncol, nlyr)
## resolution  : 30, 30  (x, y)
## extent      : 301905, 335745, 4111245, 4154085  (xmin, xmax, ymin, ymax)
## coord. ref. : WGS 84 / UTM zone 12N (EPSG:32612) 
## source      : landsat.tif 
## names       : landsat_1, landsat_2, landsat_3, landsat_4 
## min values  :      7550,      6404,      5678,      5252 
## max values  :     19071,     22051,     25780,     31961

nlyr() retrieves the number of layers stored in a SpatRaster object:

nlyr(multi_rast)

## [1] 4

For multi-layer raster objects, layers can be selected with terra::subset().⁴ It accepts a layer number or its name as the second argument:

multi_rast3 = subset(multi_rast, 3)
multi_rast4 = subset(multi_rast, "landsat_4")

The opposite operation, combining several SpatRaster objects into one, can be done using the c function:

multi_rast34 = c(multi_rast3, multi_rast4)

Geographic coordinate systems

Geographic coordinate systems identify any location on the Earth’s surface using two values — longitude and latitude (see left panel of Figure below). Longitude is location in the East-West direction in angular distance from the Prime Meridian plane. Latitude is angular distance North or South of the equatorial plane. Distances in geographic CRSs are therefore not measured in meters. This has important consequences.

The surface of the Earth in geographic coordinate systems is represented by a spherical or ellipsoidal surface. Spherical models assume that the Earth is a perfect sphere of a given radius – they have the advantage of simplicity but, at the same time, they are inaccurate: the Earth is not a sphere! Ellipsoidal models are defined by two parameters: the equatorial radius and the polar radius. These are suitable because the Earth is compressed: the equatorial radius is around 11.5 km longer than the polar radius.

Ellipsoids are part of a wider component of CRSs: the datum. This contains information on what ellipsoid to use and the precise relationship between the Cartesian coordinates and location on the Earth’s surface. There are two types of datum — geocentric (such as WGS84) and local (such as NAD83). You can see examples of these two types of datums in the figure below.. Black lines represent a geocentric datum, whose center is located in the Earth’s center of gravity and is not optimized for a specific location. In a local datum, shown as a purple dashed line, the ellipsoidal surface is shifted to align with the surface at a particular location. These allow local variations in Earth’s surface, for example due to large mountain ranges, to be accounted for in a local CRS. This can be seen in the Figure below, where the local datum is fitted to the area of Philippines, but is misaligned with most of the rest of the planet’s surface. Both datums in the Figure below are put on top of a geoid - a model of global mean sea level.

Geocentric and local geodetic datums shown on top of a geoid (in false color and the vertical exaggeration by 10,000 scale factor). Image of the geoid is adapted from the work of @essd-11-647-2019.

(ref:datum-fig)

Projected coordinate reference systems

All projected CRSs are based on a geographic CRS, described in the previous section, and rely on map projections to convert the three-dimensional surface of the Earth into Easting and Northing (x and y) values in a projected CRS. Projected CRSs are based on Cartesian coordinates on an implicitly flat surface (right panel of Figure below) They have an origin, x and y axes, and a linear unit of measurement such as meters.

This transition cannot be done without adding some deformations. Therefore, some properties of the Earth’s surface are distorted in this process, such as area, direction, distance, and shape. A projected coordinate system can preserve only one or two of those properties. Projections are often named based on a property they preserve: equal-area preserves area, azimuthal preserve direction, equidistant preserve distance, and conformal preserve local shape.

There are three main groups of projection types - conic, cylindrical, and planar (azimuthal). In a conic projection, the Earth’s surface is projected onto a cone along a single line of tangency or two lines of tangency. Distortions are minimized along the tangency lines and rise with the distance from those lines in this projection. Therefore, it is the best suited for maps of mid-latitude areas. A cylindrical projection maps the surface onto a cylinder. This projection could also be created by touching the Earth’s surface along a single line of tangency or two lines of tangency. Cylindrical projections are used most often when mapping the entire world. A planar projection projects data onto a flat surface touching the globe at a point or along a line of tangency. It is typically used in mapping polar regions. sf_proj_info(type = "proj") gives a list of the available projections supported by the PROJ library.

A quick summary of different projections, their types, properties, and suitability can be found at https://www.geo-projections.com/.

Important items to remember:

• That coordinate systems are a key component of geographic objects
• Knowing which CRS your data is in, and whether it is in geographic (lon/lat) or projected (typically meters), is important and has consequences for how R handles spatial and geometry operations
• CRSs of sf objects can be queried with the function st_crs(), CRSs of terra objects can be queried with the function crs()

Examples of geographic (WGS 84; left) and projected (NAD83 / UTM zone 12N; right) coordinate systems for a vector data type.